Question

Write a definite integral which can be approximated to be the Riemann Sum of:
1/50 ( sqrt of (1/50) + sqrt of (2/50) + sqrt of (3/50)....sqrt of (50/50) ).

Answer 1

ill write it with teh equation thing also

Answer 2

\[1/50* (\sqrt{1/50} + \sqrt{2/50}+ \sqrt{3/50}...\sqrt{50/50}) \]

Answer 3

you have any idea of where to start?

Answer 4

n=10?

Answer 5

looks like you have 50 to me

Answer 6

\[\sum_{i=1}^{50}\sqrt{\frac{i}{50}}\frac{1}{50}\]

Answer 7

so the function is sqrt of 1/50 times 1/50?

Answer 8

your function is \[f(x)=\sqrt{x}\]

Answer 9

\[\Delta x=\frac{1}{50}\]

\[x_i^*=a+i\times\Delta x=\frac{i}{50}\]
then you can write the above as

\[\sum_{i=1}^{50}f(x_i^*)\Delta x\]

Answer 10

\[\int\limits_{a}^{b}f(x)dx=\lim_{n\to\infty}\sum_{i=1}^{n}f(x_i^*)\Delta x\]

Answer 11

so wat was a in this case? 1?

Answer 12

a=0

Answer 13

b=1

Answer 14

\[\Delta x=\frac{b-a}{n}=\frac{1-0}{50}=\frac{1}{50}\]

Answer 15

srry i cant read that clearlythe limit says as wat approaches infinity?

Answer 16

yes...as n goes to infinity then we get the definite integral

Answer 17

this makes sense now! thanks for explaining teh steps b.c i was confused with how u got the asnwer

Answer 18

srry earler for sum reason i was talkin about another problem which is why i said n = 10 n etc..

Answer 19

the integral you will get in the end is


\[\int\limits_{0}^1\sqrt{x}dx\]

Answer 20

why is taht?

Answer 21

look from where I said


"your function is

\[f(x)=\sqrt{x}\]
"

Answer 22

OH!

Answer 23

ok

Answer 24

\[1/50* (\sqrt{1/50} + \sqrt{2/50}+ \sqrt{3/50}...\sqrt{50/50})\approx.676095\]

\[\int\limits_{0}^1\sqrt{x}dx=.\overline{6}\]

Answer 25

thats really cool

Answer 26

calc is mucch more fun n interesting when i actually understand it

Answer 27

yep...it's good stuff

Answer 28

i tend to b kinda slow especially wen things arent done step by step...srry

Answer 29

np